Question

For a plane travelling EM wave, the correct equation for characteristic impedance Z for the medium with permittivity of ε and permeability of μ is:
1. \(Z = \sqrt \frac {\mu}{\varepsilon}\)
2. \(Z = \sqrt \frac {\varepsilon}{\mu}\)
3. \(Z = \sqrt {(\mu * \varepsilon)}\)
4. \(Z = \frac {1}{\sqrt {\mu*\varepsilon}}\)

Answer 1

Correct Answer - Option 1 : \(Z = \sqrt \frac {\mu}{\varepsilon}\)

Explanation:

Intrinsic Impedance:

1. Intrinsic impedance of a medium can be defined as the impedance which an electromagnetic wave faces while traveling in a medium.

2. It is also defined as the ratio of the electric field to the magnetic field.

3. The intrinsic impedance of a medium is given by:

\(\Rightarrow η =\sqrt{\frac{j\omega \mu }{σ +j\omega \epsilon }}~\)  ---(1)

Where μ = Magnetic permeability of the medium.

And ϵ = Electric permittivity of the Medium.

For lossless or perfectly dielectric medium,

σ = 0 

Putting σ = 0 in equation (1) we get

\(η =\sqrt{\frac{j\omega \mu }{j\omega \epsilon }}=~\sqrt{\frac{\mu }{\epsilon }}\)

Hence option (1) is the correct solution

For free-space, the intrinsic impedance is a real quantity, i.e.

\(\eta_0=\sqrt \frac{\mu_0}{\epsilon_0} \ = \ 120\pi\)

η_o ≈ 377 Ω